Try making it even simpler. Make a file with a .php extension that contains only this:

Code:

<?php
echo "Hello world!";
?>

In your example, you are trying to embed PHP in HTML, which is valid, but my example is straight PHP, no HTML, which should work by default. If it does not work, you need to ask your hosting provider for assistance. Your hosting provider will be able to check the Apache error_log, which you do not have access to as a site owner, and find the problem.